Towards Improved Quantum Machine Learning for Molecular Force Fields

TL;DR

The paper investigates equivariant quantum neural networks (QNNs) for predicting molecular energies and forces in MD simulations, benchmarked on the rMD17 dataset. It first analyzes a baseline equivariant QNN encoding and identifies key expressivity and transferability limitations, notably the lack of species information and short-range behavior. A revised angular-radial QNN encoding with species-pair-dependent parameters is proposed to address these issues, along with a decoupled angular/radial parameterization to preserve SO(3) symmetry. Despite improved force predictions and reduced overfitting, energy predictions remain weak and the models fail to exhibit meaningful scaling with data, underscoring fundamental challenges and guiding future work toward richer encodings, permutation handling, and hybrid quantum-classical approaches.

Abstract

This study explores the use of equivariant quantum neural networks (QNN) for generating molecular force fields, focusing on the rMD17 dataset. We consider a QNN architecture based on previous research and point out shortcomings in the parametrization of the atomic environments. These shortcomings limit its expressivity as an interatomic potential and precludes transferability between molecules. We propose a revised QNN architecture that addresses these shortcomings. While both QNNs show promise in force prediction, with the revised architecture showing improved accuracy, they struggle with energy prediction. Further, both QNNs architectures fail to demonstrate a meaningful scaling law of decreasing errors with increasing training data. These findings highlight the challenges of scaling QNNs for complex molecular systems and emphasize the need for improved encoding strategies, regularization techniques, and hybrid quantum-classical approaches.

Figures (10)

• Figure 1: The encoding circuit together with the initial state $\ket{\psi}$ to produce the state $\ket{R_i}$.
• Figure 2: The full circuit diagram given by the function \ref{['eqn:measurement']}, the encoding circuit $\Phi(R_i)$ is given in \ref{['fig:encoding']}, the layer $\mathrm{L}_d(R_i)$ in \ref{['eqn:layer']} and the measurement operator H$^{(1, 2)}$ in \ref{['eqn:to_measure']}.
• Figure 3: The modified encoding circuit to build $\ket{R_i, S_i}_{\mathrm{a}}$ (top) and $\ket{R_i, S_i}_{\mathrm{r}}$ (bottom). Note that the starting state of the angular register is $\ket{\psi}=\bigotimes_{i=1}^{N_{\mathrm{q}}/2} \ket{S}$.
• Figure 4: A single RYCX$(\vec{\theta})$ block of parametrized circuits applied to the radial register. The radial parameter layer $\mathrm{L}_d^{(r)}(R_i, S_i)$ consists of two such blocks, followed by a radial encoding layer (\ref{['fig:modified_encoding']}).
• Figure 5: The modified QNN architecture.